Racing Suspension - Stock Car Dynamics, Part 1

1/13Front-running teams in every series have developed methods of finding the perfect balanced setup. Now some of these methods are being taught around the world.

In the May '03 issue of Circle Track, we ran Part One of a three-part story on stock car vehicle dynamics. Since we all tend to forget, we decided it was time to refresh our memories a bit. Since that time, many successful dirt and asphalt teams have applied the technology presented then to become more successful in their racing endeavors.

The early evolution of the knowledge of vehicle dynamics ran directly parallel to the development of the passenger cars and trucks for several understandable reasons. First and foremost, the big automakers had the funds to finance the extensive and expensive research. Also, the need existed to develop better suspension systems for ride comfort as well as drivability. Along with these two driving forces also existed the element of competition to develop more advanced cars than the other automakers in order to enhance their sales.

Early pioneers of stock car dynamic research include Maurice Olley and his group, whose work represented much of the significant progress that had been made in vehicle dynamic research. Among many other notable accomplishments, his work in the early '30s led the industry to adapt the double A-arm suspension system, or short long-arm (SLA) suspensions.

2/13Shown are sketches from the Advanced Dynamics seminar given by Claude Rouelle.

In 1952, Bob Schilling, the head of the mechanical engineering department in the GM Research Laboratory division, and his group met with a group of aircraft engineers that included Bill and Doug Milliken. The aero engineers were then contracted by GM to attempt to apply techniques that had been used in aircraft design to the study of land vehicle dynamics.

A compilation of that work, as well as other research, is contained in a book published by the Society of Automotive Engineers (SAE) titled Race Car Vehicle Dynamics.

During the period between the late '40s and the early '90s, no one had completely developed a way to predict how a stock car would handle and therefore be able to adjust the suspension components to attain that perfectly balanced setup. We knew that if we could ultimately predict the distribution of weight on the tires when the car was executing the turn, we would know how the car would handle.

What has been refined in most top racing series over the years is the art of trial and error. Advanced measuring systems are in use today that not only record movements, pressures, and temperatures, but also the forces exerted on components. These systems have become useful and necessary tools of the modern day chassis tuner and developer. As the teams compile and study all of this information, the fact still remains that many teams tend to react to, and not necessarily predict, the handling nature of their cars.

3/13Roll axis/roll couple distribution technology was primarily developed for symmetrical suspension systems such as those found in production automobiles. This method involves calculating the resistance to roll of each suspension system. It does not take into account all of the dynamic effects associated with a race vehicle.

Technology related to the ability to predict the handling characteristics of your car has now evolved. It is a continuation and refinement of the work that early vehicle dynamics pioneers such as Olley started. Without their efforts, none of what we have learned over the past 10 years could exist.

Let's go back and see how chassis technology progressed through the '50s up to the early '90s. Much of the research was undertaken by the engineers who were either working for or contracted by the automakers, with a heavy contribution by the General Motors group.

The primary thread of their analysis of vehicle dynamics involved a model of a vehicle that treated the body and frame as a single unit with a single center of gravity (CG) for the sprung mass. The roll centers at the front and rear were connected by an invisible line or axis, and a right-angle line between the CG and the roll axis was the vehicle's moment arm. This is basically aeronautical engineering technology that is used to simulate how aircraft maneuver and respond to various rolling forces during flight.

4/13The roll angle analysis method allows us to predict how each end of the car wants to react to the force created by cornering. If we know what each end wants to do and can alter the suspension components, such as spring rates and moment center (previously referred to as roll center) locations, then we can design our car to have a balanced setup prior to testing or racing.

A moment arm is much like a prybar or shovel handle. The CG is equivalent to the end of the bar we hold on to, and the roll centers and axis form the opposite end, which is the object we are trying to move. The longer the bar (moment arm), the more leverage we have, and the easier we can move the object (or in this case, roll the car). The bottom of the moment arm is what we have named the moment center. The older technology refers to this point as the roll center, but because the chassis almost never rolls around this point, we coined a new name for it.

In the roll axis thread of technology, each end of the car was calculated to have a given roll-resistance percentage based on the spring rates and other pertinent information. In theory, a car that had 50 percent front and rear roll resistance should have been balanced. In subsequent skid-pad testing, a neutral-handling car was found to have significantly different roll couple numbers at the front and rear.

The handling characteristics and roll couple of the car could be altered by changing the couple percentage at each end, but the handling still could not be predicted. The cars were dialed in through trial-and-error methods. The roll couple distribution thread of vehicle dynamic analysis did not present a completely accurate model that could predict a stock car's handling performance.In the early '90s, research continued and the early model was refined until an improved method was developed that represented a more accurate model. It involved treating the vehicle as two separate masses, each with its own separate suspension system. The roll couple was now measured as roll angles. This solved basic errors in predicting the roll resistance.

5/13This simple diagram shows the two ends of the moment arm. The front roll angle is a product of the height and magnitude of the center of gravity/centrifugal force. The moment center resists this force. The length of the moment arm influences how much the front wants to roll.

This method made a lot of practical sense because we have two axles in a stock car, each supporting the weight of one end of the car, and each resisting the lateral forces created by cornering. In physics, we are taught that everything is fluid or somewhat flexible. Dividing the car into separate halves allows us to analyze each one independently to determine its desire.

If you will remember, we recently did a story that covered an advanced seminar given by race engineer Claude Rouelle. We discovered that he teaches this very same method and, to our surprise, the use of this method has become much more universal than we could have imagined when we wrote about it in 2003.

The method helps us to determine the components we need in order to create a balanced setup. These components consist of the spring rates, the moment center locations (front and rear), and the weight distribution.

6/13A more realistic picture of what goes on in a stock car as we negotiate a turn takes into account the banking angle of the racetrack as well as the vertical and lateral location of the moment center. The centrifugal force combines with the gravitational force that exists all of the time to produce a resultant force. We use the magnitude and direction of the resultant force to determine the effective moment arm length.

There are several critical reasons that a balanced setup is essential to optimum chassis performance. First of all, we can accurately predict the weight transfer if the setup in the car is balanced. An unbalanced car redistributes the weight on the four tires in a very unpredictable way. If we cannot determine the desires of each end of the car, balanced or not, we cannot accurately predict the exact amount of weight transfer and, ultimately, how much weight ends up on each tire at mid-turn.

Unbalanced setups abuse one or more tires. It is this abuse that causes the tires to wear or heat up excessively. Balanced setups distribute the weight and workload evenly on each pair of tires.

It is important to note here that this method, although fairly new in concept, has been applied successfully to stock cars for many years. Cars representing every class of stock cars have had this method applied to them with predicted results. In other words, when the cars were balanced, they became fast and consistent, and this showed in the even tire temperatures front to rear at each side. The lap times became very consistent and the cars handled very well.

7/13When the moment center is located to the left of the centerline between the front tires, the effective moment arm is relatively long. This promotes a larger roll angle at the front and makes the front more efficient.

The primary front suspension systems that are used today are the double A-arm (the most common), the solid axle, and more recently, the strut, with the top of the shock acting as a substitute for an upper A-arm. The solid axle system reacts just like a rear differential system, so it will be included in the rear suspension discussion.

A double A-arm suspension has a moment center that represents the bottom of the moment arm. The top of the moment arm is the center of gravity of the sprung mass of the front of the car. As the center of gravity/center of mass tries to continue in a straight line as we turn the corner, a lateral force (centrifugal force) is exerted on the chassis, and that force is resisted by the moment center.

If you stick a shovel blade firmly into the ground and then pull on the end of the handle, your arms represent the lateral g-force, the end of the shovel handle is the center of gravity, and the blade at the ground is the moment center. The handle of the shovel is the moment arm.

8/13Many stock cars have a front geometry design that puts the moment center to the right of the centerline between the front tires. As the MC is designed further to the right, the front suspension becomes much stiffer due to the diminishing length of the moment arm.

The most efficient way to apply a force to the shovel is to pull the handle at a right angle. In a double A-arm suspension, this is almost never the case. Usually the resultant force (a combination of the lateral force and gravity) is not perpendicular to the moment arm.

In a stock car, we really have two forces being applied to the top end of the moment arm/center of gravity. One is the lateral force of cornering known as centrifugal force, and the other is gravity. These two forces combine into one resultant force for which we can calculate a magnitude and direction.

By looking at the direction of the resultant force, we can see the true picture of how the combination of the two forces react in the front suspension through the moment center. The effective moment arm is the result of the direction of the resultant force and the location of the moment center.

9/13The rear suspension is much different than the front suspension. The spring base is felt at the top of the springs. The moment center resists the lateral centrifugal force that causes the suspension to roll. Changing the MC height, rear spring rates, and spring split are the primary methods used to adjust the rear roll angle.

The effective moment arm is the right-angle distance between the resultant force line and the moment center. This is very important because we can see that when the moment center is moved to the right or left, the effective moment arm length changes. As in the shovel handle analogy, a longer handle can apply more force to the end, just as a longer effective moment arm applies more force to roll our stock car.

The amount of lateral force and the length of the effective moment arm are contributing factors that help us predict exactly what roll angle the front of our car desires. If the front end of our car was not rigidly connected to the rear, it would roll to a predicted angle and a predictable amount of load would transfer from the left-front tire onto the right-front tire. But that is not the case. The two are connected, and we cannot accurately predict the weight transfer at each end of the car unless we know the desires of each end.

10/13The rear moment center height of a Panhard/J-bar system is the average height of the two ends of the bar. For the purpose of roll angle prediction, the MC is located laterally halfway between the top of the springs and at a height that is the average height of the two ends.

Both suspension systems of the car are connected by a rigid chassis, however stiff this connection may be, and what each desires to do is influenced by what the other wants to do. I have used an analogy in the past that helps to explain this concept. Have you ever seen a circus act in which two people are in a horse suit? The horse moves around well, as long as each end is in sync with the other. When the rear wants to go left and the front wants to go right, it gets comical. In our stock car, when the front moves/rolls differently than the rear, it is not so funny and performance suffers.

There are six primary factors influencing the amount of roll angle in the front suspension. They are as follows: 1) The weight of the sprung mass of the car supported by the front suspension. This is represented by the weight of the front end measured on the scales under the left-front and right-front tires minus the unsprung weight of the wheels, tires, and so on; 2) The magnitude of the lateral force measured in g's. A 1g lateral force would equal the sprung weight of the front end; 3) The moment center location, both in height and width after the car dives and rolls in the turns; 4) The overall spring stiffness translated to wheel rate, as well as the relationship of the two spring rates side to side (i.e., softer right-front versus left-front spring, and so on); 5) The front sway bar has an effect of antiroll and must be taken into account. The larger the bar is, the more resistance there is to roll; 6) The track banking angle.

11/13A typical rear sway bar installation uses a high mount and arms with several holes used to adjust the length of the arm, which changes the rate of the assembly. Note that the link between the sway bar arm and the rear end is 90 degrees off the arm and directly above and in line with the motion of the axle tube.

The rear suspension system is much different from the front, and we look at it differently. At the front, the spring base is felt at the wheels. With a rear solid axle system (and this relates also to a front straight-axle car), we have a spring base that is felt on the top of the actual springs. This dynamic model is not a new concept-it was developed and published some 60 years ago.

Like the front suspension, the rear suspension has a center of gravity of the sprung weight of the car that represents the top of the moment arm. The bottom of the moment arm is the moment center created by the lateral locating device known to us by the terms Panhard/J-bar, metric four-link, leaf springs, or Watt's link. These four devices comprise the majority of lateral restraint systems used for straight-axle suspensions in stock cars. Each restraint system has its own moment center height that represents the bottom of the rear moment arm.

The height of the rear moment center is fairly easy to determine, but there have been varying theories on both the height and lateral location. Again, going back to early writings on the subject, the car "feels" the rear moment center laterally halfway between the two springs. Subsequent experiments have proven that regardless of the lateral location of the locating devices, the rolling force remains the same, thus proving the early publications.

Note: The car "feels" the spring base at the top of the springs. In a car with coilover springs, the distance between the tops of the mounting bolts is the rear spring base.

12/13The leaf spring rear locating device is unique in that the mounting points of the springs are also the lateral locating devices. Therefore, the average heights of the ends equal the height of the rear moment center. The leaf-spring system provides a wide spring base and is superior to other suspension systems in some respects.

There are additional effects created by the Panhard/J-bar angle that tend to leverage and exert influential forces on the suspension, and those effects will be covered in future articles on chassis dynamics.

There are seven primary factors that affect the magnitude of the rear-roll angle. These are: 1) The sprung mass of the portion of the car supported by the rear suspension (scale weights at the LR and RR tires minus unsprung components); 2) The height of the rear moment center; 3) The magnitude of the lateral force; 4) The overall spring stiffness as well as side-to-side spring split; 5) The width of the spring base, which is the distance between the centers of the top of the springs; 6) The rear sway bar (if used) has a large effect of antiroll and must be taken into account; 7) The track banking angle.

Now that we know the importance of matching the desires of each suspension system, the key to creating a balanced setup is to change springs and moment center locations so that each end of the car will want to have the same desires. The result of doing that is a faster race car that is more consistent in handling balance.

13/13The Watt's link is mostly used in road racing cars. The advantage of this system is that the rear solid axle does not move laterally as the chassis moves vertically. With some three-link and metric four-link support systems, lateral movement of the rear end would cause adverse rear steer. The Watt's system eliminates the lateral movement that creates the rear steer. The rear moment center location also stays very consistent with right and left turns encountered in road racing.

In next month's issue, we will examine how we can apply this technology to set up some typical types of stock cars. Understanding these basic principles of stock car dynamics will help you make correct setup decisions.

A sway bar is a device that produces a resistance to roll when used in either the front double A-arm or straight-axle suspension system. Its influence in a double A-arm suspension is much less than when used in the solid-axle suspension.

The sway bar has a stabilizing effect on the double A-arm system and helps control oscillations that are common with that type of suspension. The sway bar is more effective in a straight-axle suspension when, for reasons of design limitations, the rear-roll angle is hard to control. Such is the case with big-spring/truck-arm suspensions like those used in Nextel Cup cars.

The tendency in recent years for asphalt circle track racing has been to use softer spring setups and stiffer sway bars. Racers have found both success and limitations to the usefulness of this trend. In some cases, they have found that softer springs and larger diameter sway bars help to lower the car's center of gravity and to also promote an efficient aerodynamic configuration when the car is at racing speeds.